The word "elements" in the title of this book does not convey the
implica- tion that its contents are "elementary" in the sense of "easy"
it mainly means that no prerequisites are required, with the exception
of some basic background in classical physics and calculus. It also
signifies "devoted to the foundations". In fact, the arguments chosen
are all very classical, and the formal or technical developments of this
century are absent, as well as a detailed treatment of such problems as
the theory of the planetary motions and other very concrete mechanical
problems. This second meaning, however, is the result of the necessity
of finishing this work in a reasonable amount of time rather than an a
priori choice. Therefore a detailed review of the "few" results of
ergodic theory, of the "many" results of statistical mechanics, of the
classical theory of fields (elasticity and waves), and of quantum
mechanics are also totally absent; they could constitute the subject of
two additional volumes on mechanics. This book grew out of several
courses on meccanica razionaie, i.e., essentially, theoretical
mechanics, which I gave at the University of Rome during the years
1975-1978.